A straightening-unstraightening equivalence for $\infty$-operads
A straightening-unstraightening equivalence for $\infty$-operads
We provide a straightening-unstraightening adjunction for $\infty$-operads in Lurie's formalism, and show it establishes an equivalence between the $\infty$-category of operadic left fibrations over an $\infty$-operad $\mathcal{O}^\otimes$ and the $\infty$-category of $\mathcal{O}^\otimes$-algebras in spaces. In order to do so, we prove that the Hinich-Moerdijk comparison functors induce an equivalence between …